Recursion HALP

Hey /prog/, I must say my understanding of recursion is shit (never really dealt with recursion in all my days of writing bad code). How should I go about thinking about it?

inb4 flaming: I understand the recursive concept in some contexts, such as when it is used in a factorial function, but when it starts getting more ambiguous (say, exercise 5, ch. 2 from ANSI Common Lisp) it's ugly.

inb4 RECURSE MY ANUS

You still haven't answered the questions. Is the variable a variable in the C/C++ sense or the math sense? You're shit diagram doesn't say. Again, for the third time, and what point and time do you evaluate fact? I don't see this in your shit diagram. Again, for the third time, what point and time do you do the multiplications? Again, your shit diagram doesn't tell.

And again, until you can answer my questions, your silence will just reaffirm my belief that you are some uneducated nigger that has never done any kind of real programming for a living.